In a coherent optical transmission link, a signal proportional to the envelope of the optical electric field is detected. Thus modulation by data implicates phase, amplitude and polarization of the optical field. At near zero residual channel memory the field envelope of a single modulated carrier is a sequence of signaling intervals each characterized by a complex number (amplitude and phase) and polarization which are a representation of the data. Each signaling interval allows one of a constellation of such values where the constellation affects channel capacity. Given a channel capacity and for a linear channel, best performance is obtained for modulations with combined largest minimum Euclidean and lowest proximate Hamming distance normalized over instances of the constellation, weighted according to probability of occurrence. In the presence of optical nonlinearities, further performance optimization requires that the power variance and degree of polarization over signaling intervals be a minimum.
Known methods of performance optimization based on Euclidean/Hamming distances include high dimension sphere packing, set partitioning and trellis coding, Gray labelling, and constellation shaping. Recently, solutions which optimize performance including effects of optical nonlinearity have been devised. For example, co-pending and co-assigned U.S. patent application Ser. No. 13/969,694 filed Aug. 19, 2013 (now U.S. Pat. No. 9,143,238) and Ser. No. 14/644,320 filed Mar. 11, 2015 (published as US 2015/0195045) describe polarization-balanced and power balanced modulation formats that are tolerant of non-linear impairments of an optical transmission system. In both of these applications, the modulation is based on a multi-dimensional symbol constellation that encodes a plurality of bits over multiple signaling intervals. These applications demonstrate that modulation formats applicable to coherent optical transmission systems may be designed so as to reduce the nonlinear interference between co-propagating Wavelength Division Multiplexed (WDM) channels. In particular, so-called power balanced formats, in which each symbol of the constellation alphabet has the same energy, have been shown to reduce inter-channel nonlinear effects such as cross phase modulation (XPM).
Other known multi-dimensional modulation formats are described in: A. Shiner, et al., “Demonstration of an 8-dimensional modulation format with reduced inter-channel nonlinearities in a polarization multiplexed coherent system”, Opt. Express, 22(17), pp. 20366-20374 (2014); M Chagnon, et al. “Analysis and experimental demonstration of novel 8PolSK-QPSK modulation at 5 bits/symbol for passive mitigation of nonlinear impairments”, Opt. Express 21(25), pp. 30204-30220 (2013); and K. Kojima, et al., “Constant modulus 4D optimized constellation alternative for DP-8QAM”, In Proc. ECOC 2014, TR2014-083 (2014).
In a linear channel with Additive White Gaussian Noise (AWGN), the 8PolSK-QPSK power balanced format presented by M. Chagnon et al. increases the ideal back-to-back Required Signal-to-Noise Ratio (RSNR) by ≧0.3 dB relative to other, amplitude modulated formats at 5 bits/interval spectral efficiency and ≧3% uncoded bit error rates (BER) applicable to known Forward Error Correction (FEC) techniques. In this case, the performance gains realized through the reduction of nonlinear interference are at least partially offset by this format's increased sensitivity to additive noise.
The technique described by Kojima et al. provides a power balanced modulation format at 6 bits/interval spectral efficiency equivalent to dual polarization 8 quaternary amplitude modulation (DP-8QAM). Further, the format of Kojima et al. improves the ideal back-to-back RSNR for an uncoded BER of 1% by about 0.38 dB relative to standard DP-8QAM. However, this RSNR improvement is reduced to less than ˜0.1 dB at an uncoded BER≧3%, which is commonly encountered in practical optical networks. In addition, the higher-order phase shift keying (PSK) employed in the format of Kojima et al. can be problematic for optical carrier phase recovery in a high phase noise environment. As such, the techniques of Kojima et al. are expected to be of limited use in practical optical communications networks.
To date, modulations which have been commercialized in coherent optical transmission network systems include BPSK, polarization-switched QPSK (also referred to as HEXA or 3QAM), QPSK, 4ASK, and 16QAM on two polarizations. Of these, BPSK, QPSK and 16QAM provide raw spectral efficiencies of 2 bits, 4 bits and 8 bits per signaling interval (bits/interval), respectively. What is lacking is a commercially viable nonlinear tolerant modulation having a 6 bit per signaling interval spectral efficiency.
Other possible network design solutions may include 1) DP-16QAM operating at 0.5×symbol rate with moderately increased WDM channel spacing to achieve a spectral efficiency comparable to a 6 bit/interval format, or 2) DP-QPSK at 1.5×symbol rate to achieve comparable transmission capacity. In the first case, the ideal back-to-back RSNR of DP-16QAM is 2.39 dB worse than DP-8QAM, implying an expected (1.5×2.39)≈3.6 dB reduction in maximum system margin relative to a 6 bit/interval format, while in the second case, the spectral efficiency is reduced by 50%.
Clearly, techniques for implementing nonlinear tolerant modulation formats at 6 bit per signaling interval spectral efficiency that are usable in practical optical communications networks remain highly desirable.